1. Field of the Invention
The present invention relates to a scanning force microscope used for studying surface properties of materials on size scales ranging from the atomic to the micron level.
2. Background of the Prior Art
Scanning force microscopes (SFM) are known for their use in a broad range of fields where high resolution information regarding the surface region of a sample is desired. A certain subset of SFMs utilizes a flexible cantilever attached to a small probe. FIG. 1 shows the basic components of such an SFM. A cantilever-tip assembly 14, 15, 16 is used in conjunction with a scanning system 10, 11, 12, 13, 18, 19, 20, 21 to probe a surface 17. The tip 16 may either contact the sample or may sense the sample without direct contact. Knowledge of the position of the tip 16 is required in all modes of operation of the machine. This position is usually obtained by measuring the angular deflection of the cantilever 15 to which the tip 16 is attached. The cantilever-tip assembly is commonly modeled as a mechanical simple harmonic oscillator (SHO).
SFM, also known as Atomic force microscopes (AFM), probe the surface of a sample with a sharp tip. The tip is located at the free end of a cantilever. The length of the cantilever is generally less than 300 .mu.m. Forces between the tip and the sample surface cause the cantilever to bend, or deflect. A detector measures the cantilever deflection as the tip is scanned over the sample, or the sample is scanned under the tip. The measured cantilever deflections can be used to generate isoforce contours. Simplifying assumptions are often used to convert these isoforce curves into putative topographs of the surface. SFMs can be used to study solids and liquids, which may be insulators, semiconductors, or electrical conductors.
In addition to imaging, SFMs are used to measure forces of interaction between the probe tip and the surface. This is accomplished by performing a force-distance experiment. An SFM found in the prior art involves measurement of the position of the tip, the position of the sample, and a single value (k, the spring constant). The spring constant is then used to convert the tip and sample position information into forces.
The forces that contribute to the deflection of the SFM cantilever can be divided into two categories: repulsive and attractive. The dominant repulsive force at very short range (tip-to-sample separation &lt;0.3 nm) is the hard core repulsive force. At large separations, the tip-sample force arises from a number of physical phenomena such as electrostatics, magneto-statics, surface tension, and adhesion. One of these longer-range force terms relevant to all SPMs belongs to the electrostatics group and is commonly referred to as the van der Waals force. This force arises due to fluctuating dipoles in the tip and the sample. The dependence of the total force, which includes the van der Waals force upon the distance between the tip and the sample, is shown in FIG. 2. Two regions are labeled in FIG. 2, the contact region and the non-contact region. In the contact region, the cantilever is held less than a few tenths of a nano-meter from the sample surface, and the total inter-atomic force between the cantilever and the sample is repulsive. In the non-contact region, the cantilever is held on the order of one to ten nano-meters from the sample surface, and the inter-atomic force between the cantilever and the sample can be either attractive or repulsive.
When used as imaging tools, SPMs operate in one of two modes: variable tip position or constant tip position. In the variable mode, forces between tip and sample are allowed to alter the Z position of the tip (example: a repulsive force may push the tip up, an attractive force may pull the tip down). The point at which the tip probes the sample surface is raster scanned (this defines and X-Y plane) while the position of the tip (along the Z direction) is recorded. In this manner, a series of (x,y,z) triplets are obtained. The set of all these triplets make up the variable mode image. In the constant mode, the Z position of the tip is maintained fixed during the raster scan. Often, this is accomplished by varying the Z position of the sample during the raster scan. In this mode, the Z portion of the (x,y,z) triplet is obtained by measuring the distance the sample moves in order to maintain a constant tip position.
Cantilever based SFMs utilize three distinct sub-modes of operation which can be performed in either constant or variable mode. These sub-modes are contact, intermittent contact, and non-contact. In contact-SFM, also known as repulsive-SFM, the probe tip makes physical contact with the sample (i.e. the tip is brought close enough to the sample surface so that the dominant repulsive force is the hard core force). The tip is attached to the free end of a cantilever with a spring constant lower than the effective spring constant holding the atoms of the sample together. As the scanner gently traces the tip across the sample (or the sample under the tip), the contact force causes the cantilever to bend to accommodate changes in topography. The Z position of the cantilever is typically measured using optical techniques. The most common method involves the use of an optic lever. A laser beam is reflected off the back of the cantilever 15 and onto a position-sensitive photo-detector (PSPD) 13 as shown in FIG. 1. As the cantilever bends, the position of the laser beam on the detector shifts. The actual quantity measured is the angle through which the cantilever bends. It is common to make an approximation that any change in this angle is equal to the change in the Z-displacement of the free end of the cantilever. Other methods to detect the cantilever deflection are known. These include optical interference, a tunneling microscope, and the use of a cantilever fabricated from a piezo-electric material.
An SFM can also be operated in a mode where the tip is not in direct contact with the sample surface (i.e. the dominant repulsive force is not the hard core repulsion). Conceptually, the simplest method utilizing non-contact mode involves placing the tip far enough above the surface so that the force generated by the cantilever at its equilibrium deflection is sufficient to counter the sum of all attractive forces. The tip-sample separation (usually a few nano-meters) must be small enough so that the force field generated by the sample is sufficient to measurably deflect the cantilever. This spacing is indicated on the van der Waals curve of FIG. 2 as the non-contact region. The sample is then raster scanned below the tip and the tip displacement is recorded as in the variable contact mode technique. Prior art shows this to be the only non-contact mode to work in fluid. It is difficult to implement. A more common non-contact technique involves oscillating the cantilever near its resonant frequency. The tip sample distance it then reduced until the existence of tip-sample forces causes a shift in the resonant frequency of the cantilever. Rarely is the actual frequency shift measured. Usually, either the amplitude of vibration at the original resonant frequency is measured or the shift in phase between the driving signal and the cantilever oscillation is measured. A major shortcoming of the oscillating non-contact mode is that it does not provide the kind of high lateral resolution obtained in contact mode. Generally, lateral resolution around 10 nano-meters is obtained. NC-SFM is desirable because it provides a means for measuring sample topography with no contact between the tip and the sample and thus renders minimal damage to the sample. It is also desirable because it permits the use of extremely high signal to noise ratio instrumentation (i.e. lock-in amplification) to be used in detecting the effect of sample forces on tip position. These techniques involve measuring averages of the cantilever motion. Thus, it is desirable to have the highest possible resonant frequency so that physically meaningful averages can be taken at reasonable raster scanning rates. Typically, cantilevers with spring constants around 100 N/m having resonant frequencies in the range of 300-600 kHz are utilized. Like contact SFM, non-contact SFM can be used to measure the topography of insulators and semiconductors as well as electrical conductors. The total force between the tip and the sample in the non-contact region is very low, generally about 10.sup.-12 N. This low force is advantageous for studying soft or elastic samples. A further advantage is that samples like silicon wafers are not contaminated through contact with the tip, a very advantageous characteristic for the microelectronics industry.
Intermittent contact mode is a hybrid of the contact and non-contact modes. In this mode, the cantilever is also made to oscillate near its resonant frequency. The amplitude of oscillation is typically tens to hundreds of nano-meters. A tip-sample separation is chosen so that, at the bottom of its stroke, the probe tip comes into direct contact with the sample surface. Prior art does not describe in detail how the physical interaction between the tip and sample generates the signal measured in intermittent contact mode. In general, it can be said that some combination of the long range force of interaction and the hard core repulsion experienced at the bottom of each stroke conspire to alter the vibrational amplitude of the cantilever. Usually, this change is toward smaller amplitudes. When operated in air, intermittent contact mode is usually performed with a stiff cantilever like that used in non-contact mode. A major benefit of intermittent contact mode is that it works well in fluid. When performed in fluid, lower resonant frequency cantilevers are used (10-100 kHz) to prevent viscous damping forces from extinguishing the signal. A major advantage of intermittent contact mode is that it routinely provides very high lateral resolution (almost as high as contact mode) but does not present high shear forces in the XY plane. This permits imaging of delicate samples that are easily pushed around on the surface (example: cell membranes and adsorbed molecules).
The relationship between the motion of a cantilever and variations in sample topography can be explained as follows within the SHO model approximation. The cantilever is modeled as an oscillator having a resonant frequency that varies as the square root of its spring constant. In addition, the spring constant of the model oscillator varies with the force gradient experienced by the cantilever. Finally, the force gradient, which is the derivative of the force versus distance curve shown in FIG. 2, changes with tip-to-sample separation. Thus, changes in the resonant frequency of the cantilever can be used as a measure of changes in the force gradient, which reflect changes in the tip-to-sample spacing, or sample topography, and/or chemical nature. Prior art does not utilize the change in the model oscillator's spring constant when calculating cantilever force. Instead, it always utilizes the free space oscillator spring constant measured when the tip-sample separation is large enough so that the force field generated by the sample is not measurable by the instrument.
In prior art devices, the cantilever-tip assembly is modeled as a mechanical simple harmonic oscillator (SHO). Systems properly described by these models can not naturally vibrate at more than one frequency. In reality, multiple vibrational frequencies are excited during standard SFM operation. More than one frequency is present in the system precluding generalized application of the SHO theory. Thus, it is not appropriate to obtain forces from measured displacements of an SFM cantilever using Hooke's Law (F=-k.DELTA.z) unless it is known a priori that the system contains no vibrations above the first resonance. Using the linear equation (F=-k.DELTA.z) does not allow for more than one frequency. As the cantilever approaches the snap-to-contact point in the SHO model, the lowest frequency mode is lost. In reality, as the cantilever approaches the sample, and once it is beyond the snap-to-contact point (the tip-sample separation where the attractive force gradient exceeds the spring constant obtained using the SHO model) the cantilever cannot be excited in the lowest mode. In the SHO model--which uses a single mass and thus uses a single degree of freedom--measurement at and beyond the snap-to-contact point is pointless because no second frequency is available. Thus, true force-distance curves can not be obtained by simply multiplying measured cantilever displacements by some previously determined spring constant.
The problem with the prior art devices is that the cantilever is considered to be a simple harmonic oscillator (SHO), thereby limiting the speed with which data can be meaningfully collected from these machines. As an SHO, the system uses Hooke's law where F=-kx, to convert cantilever displacement measurements to tip-sample force values. The value of k is measured, the cantilever deflection is measured, and thus the force can be evaluated. The prior art devices can be used to make measurements of the surface at frequencies less than the lowest resonant mode of the cantilever. This means that forces between tip and sample during low raster speed topographs in either contact mode or the non-oscillating non-contact mode are well modeled using the prior art. In addition, force-distance measurements made at low speed are also well modeled using the prior art. However, high-speed topographs as well as force-distance measurements taken at high speed are not well modeled using the prior art. As the cantilever approaches the snap-to-contact point, one mode of vibration is lost using the SHO methods. In reality, as the tip approaches the sample, the cantilever is excited into higher modes. Since the SHO methods use a single mass having a single degree of freedom and therefore use of a single mode of vibration, these methods cannot yield accurate measurements. Beyond the snap-to-contact point, the distance from tip to sample (z) is well defined, but the value of (k) (the spring constant of the cantilever) is lost. The value of (k) is meaningless at this small distance (z).
Thus, fine static 3-dimensional measurements of topographic surfaces, such as a carbon fiber/polymer composite and a semiconductor, can be made using the SHO methods, but finer topographical measurements or real time measurements of interactions of molecules cannot be done reliably.
Another problem with the prior art devices is that the speed at which the cantilever approaches the sample must be slow enough so that the cantilever does not vibrate above its first mode. When using the Hooke's law approach to determining the force-distance relations, the force acting to flex or bend the cantilever as the tip approaches the sample increases as the distance (d) approaches the sample. The distance (d) to the sample is proportional to the force acting to bend the cantilever. If the speed of motion of the cantilever is above a certain value, then vibrations will be induced in the cantilever, and the measurements of the force will give inaccurate readings of the tip-to-sample distance (d). The prior art method can provide one data point (tip-to-sample distance) each millisecond. Thus, the prior art devices cannot scan a surface topography of an area fast enough for real-time imaging of relatively large objects like a protein. A biological living sample can move many pixels in one second. To have chemical specificity while resolving the motion of such a biological living sample, one needs to get F-distance measurements at each pixel and thus one sees that even for a modest 64.times.64.times.64 point's image, the frequency of the cantilever must be larger than 10.sup.5 voxels/sec. Under those conditions, motion containing frequencies larger than the lowest natural frequency will be excited.
The primary object of the present invention is to obtain accurate force measurements using an SPM. The specific situations in which this accuracy is desired are twofold. First, when the tip-sample separation is very small (within the snap-to-contact region). Second, when high data collection rates are desired as in high-speed imaging and/or high speed force-distance measurements.